Kazhdan-Lusztig bases and the asymptotic forms for affine q-Schur algebras

2014/07/17 by Weideng Cui, Cui, Weideng
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1407.4557

I will withdraw the claim "idempotence of the lowest two-sided ideal" in Section 6, and I am very sorry for my mistakes. Instead, I will study some relatively simple examples. arXiv admin note: text overlap with arXiv:0810.2335 by other authors

openalex publication_date 2014/07/17 · arxiv created 2014/07/31 · arxiv updated 2014/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define Kazhdan-Lusztig bases and study asymptotic forms for affine q-Schur algebras following Du and McGerty. We will show that the analogues of Lusztig's conjectures for Hecke algebras with unequal parameters hold for affine q-Schur algebras. We will also show that the affine q-Schur algebra S_q,k^\vartriangle(2,2) over a field k has finite global dimension when char k=0 and 1+q≠ 0.

Citations

• A new construction of the asymptotic algebra associated to the q-Schur algebra

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